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Abstract:

Porous biocompatible structures suitable for use as medical implants and
methods for fabricating such structures are disclosed. The disclosed
structures may be fabricated using rapid manufacturing techniques. The
disclosed porous structures has a plurality of struts and nodes where no
more than two struts intersect one another to form a node. Further, the
nodes can be straight, curved, portions that are curved and/or straight.
The struts and nodes can form cells which can be fused or sintered to at
least one other cell to form a continuous reticulated structure for
improved strength while providing the porosity needed for tissue and cell
in-growth.

Claims:

1. A porous structure comprising: a plurality of struts, each strut
comprises: a first end; a second end; and a continuous elongated body
between said first and second ends, said body having a thickness and a
length; and a plurality of nodes, each node comprises an intersection
between one end of a first strut and the body of a second strut; wherein
said porous structure is produced at least by a rapid manufacturing
technologies process.

2. The porous structure of claim 1 wherein the first and second ends of
one or more struts extend between the body of two other struts.

3. The porous structure of claim 1, wherein the body of one or more
struts comprise a plurality of nodes.

4. The porous structure of claim 1, wherein the cross-section of at least
one end of one or more struts is larger than the cross-section of a
portion of the body of said one or more struts.

5. The porous structure of claim 1 wherein at least a portion of the body
of one or more struts is curved.

6. The porous structure of claim 1 wherein the plurality of struts can be
sintered, melted, welded, bonded, fused, or otherwise connected to one
another.

7. The porous structure of claim 1 wherein a plurality of the struts and
nodes define at least one fenestration.

10. The porous structure of claim 1 wherein the cross section of one or
more struts comprises a polygon.

11. The porous structure of claim 1 wherein at least a portion of the
circumference of the cross-section is curved.

12. A method for fabricating a porous structure comprising the steps of:
creating a model of a porous structure at least in a computer generated
environment, wherein the creation step comprises: defining one or more
struts with a first end, a second end, and a continuous elongated body
between the first and second ends for each strut, selecting a thickness
and length for the body; and defining at least one node with an
intersection between one end of a first strut and the body of a second
strut for each node; and fabricating the porous structure according to
the model by exposing fusible material to an energy source.

13. The method of claim 12, further comprises the step of defining the
first and second ends of one or more struts to extend between the body of
two other struts.

14. The method of claim 12 further comprises the step of defining the
body of one or more struts to comprise a plurality of nodes.

15. The method of claim 12 further comprises the step of defining the
cross-section of at least one end of one or more struts to be larger than
the cross-section of a portion of the body of said one or more struts.

16. The method of claim 12 further comprises the step of defining at
least a portion of the body of one or more struts to be curved.

17. The method of claim 12 further comprises the step of sintering,
melting, welding, bonding, or fusing a plurality of struts to one
another.

18. The method of claim 12 further comprises the step of defining at
least one fenestration in the porous structure using a plurality of the
struts and nodes.

19. The method of claim 12 wherein the fabricating step further comprises
selecting a material for fabricating the one or more struts from the
group consisting of metal, ceramic, metal-ceramic (cermet), glass,
glass-ceramic, polymer, composite and combinations thereof.

21. The method of claim 12 further comprises the step of defining the
cross section of one or more struts with a polygon.

22. The method of claim 12 further comprises the step of defining at
least a portion the circumference of the cross-section with a curved
portion.

23. A porous structure comprising: at least one cell comprising: a
plurality of sides, each side comprising a polygon, wherein each leg of
the polygon comprises a strut; wherein the strut comprises: a first end;
a second end; and a continuous elongated body between said first and
second ends, said body having a thickness and a length; and a plurality
of nodes, each node comprises an intersection between one end of a first
strut and the body of a second strut.

24. The porous structure of claim 23 further comprising: a plurality of
cells coupled to one another in a stacked pattern wherein at least two
cells share one side.

Description:

[0001] The present application claims the benefit of U.S. Provisional
Patent Application No. 61/235,269, filed Aug. 19, 2009 and entitled
"Porous Implant Structures," the disclosure of which is incorporated by
reference herein in its entirety.

FIELD OF INVENTION

[0002] The present invention generally relates to porous structures
suitable for medical implants, and more particularly to porous structures
suitable for medical implants that have improved combinations of
strength, porosity and connectivity and methods for fabricating such
improved porous structures.

BACKGROUND

[0003] Metal foam structures are porous, three-dimensional structures with
a variety of uses, including medical implants. Metal foam structures are
suitable for medical implants, particularly orthopedic implants, because
they have the requisite strength for weight bearing purposes as well as
the porosity to encourage bone/tissue in-growth. For example, many
orthopedic implants include porous sections that provide a scaffold
structure to encourage bone in-growth during healing and a weight bearing
section intended to render the patient ambulatory more quickly.

[0004] Metal foam structures can be fabricated by a variety of methods.
For example, one such method is mixing a powdered metal with a
pore-forming agent (PFA) and then pressing the mixture into the desired
shape. The PFA is removed using heat in a "burn out" process. The
remaining metal skeleton may then be sintered to form a porous metal foam
structure.

[0005] Another similar conventional method include applying a binder to
polyurethane foam, applying metal powder to the binder, burning out the
polyurethane foam and sintering the metal powder together to form a
"green" part. Binder and metal powder are re-applied to the green part
and the green part is re-sintered until the green part has the desired
strut thickness and porosity. The green part is then machined to the
final shape and re-sintered.

[0006] While metal foams formed by such conventional methods provide good
porosity, they may not provide sufficient strength to serve as weight
bearing structures in many medical implants. Further, the processes used
to form metal foams may lead to the formation of undesirable metal
compounds in the metal foams by the reaction between the metal and the
PFA. Conventional metal foam fabrication processes also consume
substantial amounts of energy and may produce noxious fumes.

[0007] Rapid manufacturing technologies (RMT) such as direct metal
fabrication (DMF) and solid free-form fabrication (SFF) have recently
been used to produce metal foam used in medical implants or portions of
medical implants. In general, RMT methods allow for structures to be
built from 3-D CAD models. For example, DMF techniques produce
three-dimensional structures one layer at a time from a powder which is
solidified by irradiating a layer of the powder with an energy source
such as a laser or an electron beam. The powder is fused, melted or
sintered, by the application of the energy source, which is directed in
raster-scan fashion to selected portions of the powder layer. After
fusing a pattern in one power layer, an additional layer of powder is
dispensed, and the process is repeated with fusion taking place between
the layers, until the desired structure is complete.

[0008] Examples of metal powders reportedly used in such direct
fabrication techniques include two-phase metal powders of the copper-tin,
copper-solder and bronze-nickel systems. The metal structures formed by
DMF may be relatively dense, for example, having densities of 70% to 80%
of a corresponding molded metal structure, or conversely, may be
relatively porous, with porosities approaching 80% or more.

[0009] While DMF can be used to provide dense structures strong enough to
serve as weight bearing structures in medical implants, such structures
do not have enough porosity to promote tissue and bone in-growth.
Conversely, DMF can be used to provide porous structures having enough
porosity to promote tissue and bone in-growth, but such porous structures
lack the strength needed to serve as weight bearing structures. Other
laser RMT techniques are similarly deficient for orthopedic implants
requiring strength, porosity and connectivity.

[0010] As a result of the deficiencies of metal foam implants and implants
fabricated using conventional DMF methods, some medical implants require
multiple structures, each designed for one or more different purposes.
For example, because some medical implants require both a porous
structure to promote bone and tissue in-growth and a weight bearing
structure, a porous plug may be placed in a recess of a solid structure
and the two structures may then be joined by sintering. Obviously, using
a single structure would be preferable to using two distinct structures
and sintering them together.

[0011] In light of the above, there is still a need for porous implant
structures that provide both the required strength and desired porosity,
particularly for various orthopedic applications. This disclosure
provides improved porous structures that have both the strength suitable
for weight bearing structures and the porosity suitable for tissue
in-growth structures and a method for fabricating such improved porous
structures.

SUMMARY OF THE INVENTION

[0012] One objective of the invention is to provide porous biocompatible
structures suitable for use as medical implants that have improved
strength and porosity.

[0013] Another objective of the invention is to provide methods to
fabricate porous biocompatible structures suitable for use as medical
implants that have improved strength and porosity.

[0014] To meet the above objectives, there is provided, in accordance with
one aspect of the invention, there is a porous structure comprising: a
plurality of struts, each strut comprises a first end, a second end; and
a continuous elongated body between the first and second ends, where the
body has a thickness and a length; and a plurality of nodes, each node
comprises an intersection between one end of a first strut and the body
of a second strut.

[0015] In a preferred embodiment, the first and second ends of one or more
struts extend between the body of two other struts. In another preferred
embodiment, the body of one or more struts comprise a plurality of nodes.

[0016] In accordance with another aspect of the invention, there is a
porous structure comprising a plurality of struts, wherein one or more
struts comprise a curved portion having a length and thickness; a
plurality of junctions where two of said curved portions intersect
tangentially; and a plurality of modified nodes, each modified node
comprises an opening formed by three or more of said junctions.

[0017] In a preferred embodiment, the porous structure includes at least
one strut comprising a straight portion having a length and a thickness.
In another preferred embodiment, the porous structure includes at least
one strut having a first end, a second end; and a continuous elongated
body between the first and second ends, where the body has a thickness
and a length; and at least one closed node comprising an intersection
between one end of a first strut and the body of a second strut, wherein
the strut can comprise of a straight portion, a curved portion, or both.

[0018] In accordance with another aspect of the invention, there are
methods for fabricating a porous structure. One such method comprises the
steps of: creating a model of the porous structure, the creation step
comprises defining a plurality of struts and a plurality of nodes to form
the porous structure and fabricating the porous structure according to
the model by exposing metallic powder to an energy source. The defining
step comprises the steps of providing a first end, a second end; and a
continuous elongated body between the first and second ends for each
strut, selecting a thickness a length for the body; and providing an
intersection between one end of a first strut and the body of a second
strut for each node.

[0019] In a preferred embodiment, the method includes defining the first
and second ends of one or more struts extend between the body of two
other struts. In another preferred embodiment, defining the body of one
or more struts to comprise a plurality of nodes.

[0020] In accordance with another aspect of the invention, a second method
for fabricating a porous structure comprises the steps of: creating a
model of the porous structure; the creation step comprises selecting at
least one frame shape and size for one or more cells of the porous
structure, where the frame shape comprises a geometric shape selected
from the group consisting of Archimedean shapes, Platonic shapes,
strictly convex polyhedrons, prisms, anti-prisms and combinations
thereof; adding one or more struts to the frame where the struts
comprises a curved portion, said adding step is performed by inscribing
or circumscribing the curved portion of the one or more struts within or
around one or more faces of the selected shape; selecting a thickness for
the frame and the one or more struts; and fabricating the porous
structure according to the model by exposing metallic powder to an energy
source.

[0021] In a preferred embodiment, the creation step includes the step of
removing a portion of the frame from one or more cells of the model. In
another preferred embodiment, the fabrication step includes defining
N.sub.(1, x) layer-by-layer patterns for the porous structure based on
the selected dimensions, at least one cell shape and at least one cell
size, where N ranges from 1 for the first layer at a bottom of the porous
structure to x for the top layer at a top of the porous structure;
depositing an Nth layer of powdered biocompatible material; fusing
or sintering the Nth pattern in the deposited Nth layer of
powdered biocompatible material; and repeating the depositing and fusing
or sintering steps for N=1 through N=x.

[0022] In a refinement, the method may further comprise creating a model
of the porous structure wherein, for at least some nodes, no more than
two struts intersect at the same location.

[0023] In another refinement, the method may comprise creating a model of
the porous structure wherein at least one strut or strut portion is
curved.

[0024] The disclosed porous structures may be fabricated using a rapid
manufacturing technologies such as direct metal fabrication process. The
struts can be sintered, melted, welded, bonded, fused, or otherwise
connected to another strut. The struts and nodes can define a plurality
of fenestrations. Further, the struts and nodes can be fused, melted,
welded, bonded, sintered, or otherwise connected to one another to form a
cell, which can be fused, melted, welded, bonded, sintered, or otherwise
connected to other cells to form a continuous reticulated structure.

[0025] In some refinements, at least one, some, or all struts of a cell
may have a uniform strut diameter. In some refinements, one, some, or all
of the struts of a cell may have a non-uniform strut diameter. In some
refinements, a cell may have combinations of struts having uniform and
non-uniform strut diameters. In some refinements, at least one, some, or
all of the uniform diameter struts of a cell may or may not share
similar, different, or identical strut diameters, longitudinal shapes,
cross-sectional shapes, sizes, shape profiles, strut thicknesses,
material characteristics, strength profiles, or other properties. In some
refinements, one, some, or all struts within a cell may grow or shrink in
diameter at similar, different, or identical rates along a predetermined
strut length.

[0026] In some refinements, struts within a cell may extend between two
nodes. In a further refinement of this concept, struts may have varying
cross-sectional diameters along a strut length, including a minimum
diameter at a middle portion disposed between the two nodes. In further
refinement of this concept, struts may have two opposing ends, with each
end connected to a node and a middle portion disposed between the two
ends. Struts may flare or taper outwardly as they extend from the middle
portion towards each node so that a diameter of the middle portion is
generally smaller than a diameter of either or both of the two opposing
ends. In some instances, the struts may flare in a parabolic fluted shape
or may taper frusto-conically.

[0027] In other refinements, at least one, some, or all struts within a
cell are curved. In further refinement of this concept, one, some, or all
of the cells within a porous structure comprise at least one curved
strut. In further refinement of this concept, all of the struts that make
up a porous structure are curved. In further refinement of this concept,
curved struts may form complete rings or ring segments. The rings or ring
segments may be inter-connected to form open sides or fenestrations of
multiple-sided cells. In some instances, a single ring may form a shared
wall portion which connects two adjacent multiple-sided cells. In some
instances, one or more ring segments alone or in combination with
straight strut portions may form a shared wall portion which connects two
adjacent multiple-sided cells. In still a further refinement, the number
of sides of each cell may range from about 4 to about 24. More
preferably, the number of sides of each cell may range from about 4 to
about 16. One geometry that has been found to be particularly effective
is a dodecahedron or 12 sided cell. However, as explained and illustrated
below, the geometries of the individual cells or the cells of the porous
structure may vary widely and in the geometries may vary randomly from
cell to cell of a porous structure.

[0028] In another refinement, the configurations of the cells, struts,
nodes and/or junctions may vary randomly throughout the porous structure
to more closely simulate natural bone tissue.

[0032] In another refinement, the porous structure forms at least a
portion of a medical implant, such as an orthopedic implant, dental
implant or vascular implant.

[0033] Porous orthopedic implant structures for cell and tissue in-growth
and weight bearing strength are also disclosed that may be fabricated
using a near-net shape manufacturing process such as a direct metal
fabrication (DMF) process for use with metallic biomaterials or a
stereo-lithography manufacturing process for use with polymeric
biomaterials. In instances where a DMF process is utilized, a powdered
biocompatible material is provided in layers and individual particles of
one layer of powdered biocompatible material are fused or sintered
together one layer at a time. Exemplary porous structures comprise a
plurality of three-dimensional cells. Each cell comprises a plurality of
struts. Each strut may be sintered or fused to one other strut at a node.
Each node may comprise a junction of not more than two struts. The struts
and nodes of each cell define a plurality of fenestrations. Each cell
comprises from about 4 to about 24 fenestrations. At least one strut of
at least some of the cells are curved. Each cell may be fused or sintered
to at least one other cell to form a continuous reticulated structure.

[0034] Other advantages and features will be apparent from the following
detailed description when read in conjunction with the attached drawings.
The foregoing has outlined rather broadly the features and technical
advantages of the present invention in order that the detailed
description of the invention that follows may be better understood.
Additional features and advantages of the invention will be described
hereinafter which form the subject of the claims of the invention. It
should be appreciated by those skilled in the art that the conception and
specific embodiment disclosed may be readily utilized as a basis for
modifying or designing other structures for carrying out the same
purposes of the present invention. It should also be realized by those
skilled in the art that such equivalent constructions do not depart from
the spirit and scope of the invention as set forth in the appended
claims. The novel features which are believed to be characteristic of the
invention, both as to its organization and method of operation, together
with further objects and advantages will be better understood from the
following description when considered in connection with the accompanying
figures. It is to be expressly understood, however, that each of the
figures is provided for the purpose of illustration and description only
and is not intended as a definition of the limits of the present
invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] For a more complete understanding of the present invention,
reference is now made to the following descriptions taken in conjunction
with the accompanying drawing, in which:

[0036] FIGS. 1A-1B illustrate 3-D representations of an example of the
struts at a node in a porous structure of the prior art where the struts
of FIG. 1A have like diameters and the struts of FIG. 1B have different
diameters.

[0037] FIG. 2 is a SEM (Scanning Electron Microscope) microphotograph of
an example of fractured struts of the prior art.

[0038] FIGS. 3-5 illustrate 3-D representations of one embodiment of the
struts and nodes of the present invention.

[0039] FIGS. 6-8 illustrate 3-D representations of another embodiment of
the struts and nodes of the present invention where at least some of the
struts comprises a smaller cross-sectional diameter at the body portion
of the strut as compared to the cross-sectional diameter at the node.

[0041] FIGS. 10A-10F illustrate 2-D representations of various
configurations of the frame of struts and nodes in a porous structure of
the prior art.

[0042] FIGS. 11A-11F illustrate 2-D representations of the corresponding
configurations of the frame of struts and nodes of the prior art in FIGS.
10A-10F modified by one embodiment of the present invention.

[0043] FIGS. 12A-12D illustrate 3-D representations of exemplary
embodiments of the porous structure of the present invention comprising
one or more frame configurations in FIGS. 11A-11F.

[0044] FIGS. 13A-13M illustrate 2-D representations of various exemplary
configurations of the frame of the two struts of the present invention
forming a node, including frames for struts that are straight, curved, or
a combination of both.

[0045] FIG. 14 illustrates a 2-D representation of an exemplary embodiment
of the porous structure of the present invention comprising one or more
frame configurations in FIGS. 13A-13M.

[0046] FIGS. 15A-15C illustrate 2-D representations of exemplary
configurations of various curved frames and corresponding struts of the
present invention intersecting to form a node.

[0047] FIG. 16 illustrates a 3-D representation of an exemplary embodiment
of the porous structure of the present invention comprising one or more
frame configurations in FIGS. 13A-13M, including frames for struts that
are straight, curved, or a combination of both.

[0048] FIG. 17 illustrates a 3-D representation of an exemplary frame for
a generally cubical cell of the porous structure of the present
invention.

[0049] FIG. 18 illustrates a 3-D representation of an exemplary
arrangement of frames for cubical cells in FIG. 17.

[0050] FIG. 19 illustrates a 3-D representation of an arrangement of
cubical cells of the porous structure of the prior art.

[0051] FIG. 20 illustrates a 3-D representation of an exemplary
arrangement of cubical cells of the porous structure of the present
invention.

[0052] FIG. 21 illustrates a blown up view of the arrangement in FIG. 20.

[0053] FIG. 22 illustrates a 3-D representation of an exemplary frame for
a tetrahedron-shaped cell of the porous structure of the present
invention.

[0054] FIG. 23 illustrates a 3-D representation of an exemplary frame for
square-based pyramid cell of the porous structure of the present
invention.

[0055] FIGS. 24A and 24B illustrate various views of 3-D representations
of a conventional cell of the porous structure of the prior art based on
a dodecahedral shape.

[0056] FIGS. 25A and 25B illustrate various views of 3-D representations
of one embodiment of a cell of the porous structure of the present
invention also based on a dodecahedral shape.

[0057] FIGS. 26-28 illustrate 3-D representations of a frame of the
convention cell in FIGS. 24A and 24B modified by one embodiment of the
present invention.

[0058] FIGS. 29A and 29B illustrate 3-D representations of a cell of the
present invention formed from FIGS. 26-28, where FIG. 29B is a partial
view of a 3-D representation of the frame of the cell.

[0060] FIG. 31 illustrates a frame of a truncated tetrahedral cell
unfolded into a 2-D representation.

[0061] FIG. 32 illustrates the frame of FIG. 31 formed with curved struts
according to one embodiment of the present invention.

[0062] FIG. 33 illustrates the frame of a truncated octahedral cell
unfolded into a 2-D representation.

[0063] FIG. 34 illustrates the frame of FIG. 33 formed with curved struts
according to one embodiment of the present invention.

[0064] FIGS. 35A-35E illustrate 2-D representations of examples of a
circle or an ellipse inscribed within various geometric shapes according
to one embodiment of the present invention.

[0065] FIG. 36 illustrates the frame of a truncated tetrahedral cell
unfolded into a 2-D representation with circles circumscribed around each
face of the cell according to one embodiment of the present invention.

[0066] FIGS. 37A and 37B illustrate various views of 3-D representations
of another embodiment of a cell of the present invention based on a
dodecahedral shape.

[0067] FIG. 38 illustrates a 3-D representation of yet another embodiment
of a cell of the present invention based on a dodecahedral shape.

[0068] FIGS. 39A-38C illustrate various views of 3-D representations of
yet another embodiment of a cell of the present invention based on a
dodecahedral shape.

[0069] FIG. 40 illustrates a 3-D representation of an exemplary
arrangement of the cells of FIGS. 24 and 25.

[0070] FIGS. 41A and 41B illustrate various views of 3-D representations
of an exemplary arrangement of the cells of FIGS. 24, 25, and 37

[0071] FIG. 42 illustrates a 3-D representation of an exemplary
arrangement of the cells based on a truncated tetrahedral shape having
one or more curved struts.

[0072] FIG. 43 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on truncated
octahedra.

[0073] FIG. 44 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on cubes (light
grey), truncated cuboctahedra (black), and truncated octahedra (dark
grey).

[0074] FIG. 45 illustrates a 3-D representation of an exemplary
arrangement of the present invention of cells based on cuboctahedra
(black), truncated octahedra (dark grey) and truncated tetrahedra (light
grey).

[0075] FIG. 46 illustrates a frame view of the arrangement of FIG. 42.

[0076] FIG. 47 illustrates a frame view of the arrangement of FIG. 43.

[0077] FIGS. 48-50 illustrate 3-D reprsentations of a frame based an
octahedron modified by one embodiment of the present invention.

[0078] FIGS. 51A and 51B illustrate various views of 3-D representations
of a cell of the present invention formed from the frames of FIGS. 48-50.

[0079] FIG. 52 illustrates a 3-D representation of a frame based a
truncated tetrahedron.

[0080] FIGS. 53A-53D illustrate various views of 3-D representations of a
cell formed from the frame of FIG. 52 that was modified by one embodiment
of the present invention.

[0081] FIGS. 54A-54E illustrate various views of 3-D representations of an
exemplary arrangement of the cells of FIG. 53.

[0082] FIGS. 55A-55E illustrate 3-D representations of a cell formed from
a frame based on a hexagonal prism that was modified by one embodiment of
the present invention.

[0083] FIGS. 56A-56B and 57A-57B illustrate 3-D representations of an
exemplary arrangement of the cells of FIG. 55.

[0084] FIGS. 58-61 illustrate 3-D representations of frames based on a
dodecahedron modified by various embodiments of the present invention.

[0085] It should be understood that the drawings are not necessarily to
scale and that the disclosed embodiments are sometimes illustrated
diagrammatically and in partial views. In certain instances, details
which are not necessary for an understanding of the disclosed methods and
apparatuses or which render other details difficult to perceive may have
been omitted. Also, for simplification purposes, there may be only one
exemplary instance, rather than all, is labeled. It should be understood,
of course, that this disclosure is not limited to the particular
embodiments illustrated herein.

DETAILED DESCRIPTION OF INVENTION

[0086] As discussed above, Rapid Manufacturing Techniques (RMT) such as
Direct Metal Fabrication (DMF) can be used to produce porous structures
for medical implants. However, using DMF or other RMT to fabricate porous
structures can create weak areas between fenestrations of the
three-dimensional porous structure. This is mostly due to the shapes and
configurations of the cells that have been used in the prior art to form
these porous structures. In particular, fractures typically occur at
areas where struts are connected together at a node. The fractures occur
in porous structures of the prior art because the cross-sectional area of
a strut where it connects to the node is typically less than the
cross-sectional area of the resulting node. The areas where the struts
connect to their node, typically referred to as stress risers, are common
points of structural failure. The pattern of failure at the stress risers
can also occur when the molten phase of particles does not completely
melt and fuse together or when the surrounding substrate surfaces is too
cold, which causes the hot powdered material to bead up during the DMF
process. Regardless of the exact causes of strut fractures and the
resulting poor performance of porous structures of the prior art,
improved porous structures that can be fabricated using RMT, including
DMF, and other free-form fabrication and near net-shape processes (e.g.,
selective laser sintering, electron beam melting, and stereo-lithography)
are desired.

[0087] FIGS. 1A and 1B provide an illustration of where fractures may
occur. FIGS. 1A-1B illustrate an example of a porous structure with three
or four struts, respectively, connected at a single node, where the
struts of FIG. 1A have the same diameters and the struts of FIG. 1B have
different diameters. Specifically, in FIG. 1A, three struts 102 of
generally equal diameters are connected together at node 104. Three
stress risers 106 are created at the connections between the three struts
102. Because the cross-sectional diameters of struts 102 at the stress
risers 106 are less than the cross-sectional diameter of the node 104,
the stress risers 106 are locations for a typical strut failure. In FIG.
1B, three smaller struts 108 are connected to a larger strut 110 at a
node 112. Three of the four resulting stress risers are shown at 114,
which have substantially smaller cross-sectional diameters than the node
112. FIG. 2 is a SEM (Scanning Electron Microscope) microphotograph of a
structure 200 fabricated using RMT, and it shows an example of strut
fracture surfaces 202. In FIG. 2, the sample shown is occluded with build
powder 204 in the areas around the strut fracture surfaces 202.

[0088] Referring to FIGS. 3-5, various embodiments of the present
invention are shown. In FIGS. 3-5, struts 302, 402, and 502 are connected
together at their respective nodes 304, 404, and 504 in various
combinations. Each of nodes 304, 404, and 504 is a connection between
only two struts. For example, in FIG. 5, node 504a comprises a connection
between struts 502a and 502b; node 504b comprises a connection between
struts 502b and 502c; and node 504c comprises a connection between struts
502b and 502d. By reducing the number of struts 302, 402, and 502 that
meet or are connected at their respective nodes 304, 404, and 504, the
diameter or cross-sectional area where the struts 302, 402, and 502 are
connected is substantially equal to the cross-sectional area at the
respective nodes 304, 404, and 504. Therefore, the effect of the stress
risers (not shown) on the strength of the structure is lessened in the
structures illustrated in FIGS. 3-5. Consequently, the resulting
structures are substantially stronger than the structures of the prior
art illustrated in FIGS. 1A-1B.

[0089] FIGS. 6-8 illustrate alternative embodiments of the porous
structures of the present invention comprising strut and node
combinations where at least some of the struts are characterized by a
smaller cross-sectional diameter at the body of the strut than at the
stress riser. The struts 602, 702, and 802 are characterized by a fluted
or conical shape where each of struts 602, 702, and 802 flares to a wider
cross-sectional diameter as the strut approaches and connects at the
respective nodes 604, 704, and 804. The designs of FIGS. 6-8 illustrate
incorporate fluted struts 602, 702, and 802 and non-fluted struts 606,
706, and 806, where both types of struts are connected at the respective
nodes 604, 704, and 804.

[0090] Thus, each of the connections between the fluted struts 602, 702,
and 802 and the non-fluted struts 606, 706, and 806 has a cross-sectional
diameter that is essentially equivalent to the maximum cross-sectional
diameter of fluted struts 602, 702, and 802. Accordingly, the effect of
the stress risers (not shown) of the structures are thereby reduced.
Referring to FIG. 9A, it is a plan view of the struts 802 and nodes 804
in FIG. 8. FIG. 9B is a plan view of an individual node in FIGS. 6-8,
which is labeled as struts 602 and node 604 for demonstrative purposes.
Referring to FIGS. 9A-9B, the fluted struts 602, 802 have a larger or
maximum cross-sectional diameter at the ends 606, 806 that meet at the
nodes 804, 604, and a smaller or minimum cross-sectional diameter at the
middle portions. Thus, the effect of stress risers (not shown) at the
junctions between the struts fluted struts 602, 702, and 802 and the
non-fluted struts 606, 706, and 806 are reduced. Preferably, only two
struts, e.g., 602 and 606, meet any given node, e.g. 604, for added
strength.

[0091] FIGS. 10A-10F illustrate 2-D representations of various
configurations of the frame of the struts and nodes in a porous structure
of the prior art. For simplification purposes, the struts are not
represented in 3-D but rather each strut is represented by a different
line, e.g., its frame, that is either solid, bolded solid, or dashed
lines. This representation is simply exemplary and not meant to be
limiting. In the prior art, it is typical for a porous structure to have
more than two struts meeting at a node 1002, regardless whether the strut
may be straight, curved or irregular. While FIG. 10A may show two struts
meeting at a node, the stress risers of this configuration has the effect
of the stress risers at a node with four struts connecting or
intersecting one another. For example, U.S. Publication Nos. 2006/0147332
and 2010/0010638 show examples of these prior art configurations employed
to form porous structures.

[0092] In contrast, to the prior art configurations of FIGS. 10A-10F, the
present invention reduces the effect of the stress risers at the nodes by
ensuring that no more than two struts intersect at a node. Consequently,
some embodiments result in the diameter or cross-sectional area where the
struts intersect being substantially equal to the cross-sectional area at
each node, thereby reducing the effect of the stress risers on the
strength of the structure. FIGS. 11A-11F illustrate exemplary embodiments
of the present invention for modifying the corresponding configurations
of the prior art to ensure that no more than two struts intersect at a
node. As seen in FIGS. 11A-11F, each of nodes 1102 has only two struts
intersecting. For simplification purposes, only one of the numerous nodes
in 11A-11F is labeled with the number 1102. In particular, the FIGS.
11A-11F show at nodes 1102, the end of one strut intersect the body of
another strut. Further, the modification of the prior art configurations
according to one embodiment of the present invention forms a modified
pore 1104 that is open in each configuration that provides additional
porosity with added strength, which is a great improvement over the prior
art. FIGS. 12A-12D illustrate 3-D representations of exemplary
embodiments of the porous structure of the present invention formed with
one or more configurations in FIGS. 11A-11F, where the frames, e.g.,
lines, have been given a thickness to form struts. In FIGS. 12A-12D, the
porous structures have struts 1202 that intersect one another at nodes
1204 where no more than two nodes intersect at a node.

[0093] As demonstrated by FIGS. 11A-11F, the conventional nodes 1002 of
FIGS. 10A-10F are effectively being "opened" up to ensure that no more
than two struts meet at a node. In addition to reducing the effect of
stress risers at the node, this "opening" up of the conventional nodes
1002 of FIGS. 10A-10F into nodes 1102 of FIGS. 11A-11F has the added
benefit of reducing heat variations during the fabrication process. As
with any other thermal processes, being able to control the heat
variations, e.g., cooling, of the material is important to obtain the
desired material properties.

[0094] Referring to FIGS. 13A-13M, the present invention also provides for
embodiments that reduce the effect of stress risers by incorporating
curved struts into the porous structures. FIGS. 13A-13M illustrate 2-D
representations of these various exemplary configurations of the frame of
the two struts of the present invention forming a node, including frames
for struts that are straight, curved, or a combination of both. As shown,
only two struts intersect each other at the node 1302. At least in FIGS.
13A-13C, the struts intersect one another tangentially at the node 1302,
providing increased mechanical strength and bonding. FIG. 14 illustrates
2-D representation of an exemplary embodiment of the porous structure of
the present invention comprising one or more frame configurations in
FIGS. 13A-13M, including frames for struts that are straight, curved, or
a combination of both. As shown by FIG. 14, no more than two struts,
whether curved or straight, meet at each node. FIGS. 15A-15C illustrate
2-D representations of exemplary configurations of the present invention
of various curved frames and corresponding struts intersecting to form a
node 1502. In FIGS. 15A-15C, the dashed lines represent the frames 1504
and the solid lines represent the corresponding struts 1506. As shown,
node 1502a is formed where the circular strut with its center at 1508
tangentially intersect or meet the circular strut with its center at
1510. The node 1502b is formed where the circular strut with its center
at 1508 tangentially intersect or meet the circular strut with its center
at 1512. Similarly, FIG. 15B shows the circular strut with its center at
1514 tangentially intersecting the circular strut with its center at 1516
to form node 1502c. Likewise, FIG. 15C shows the circular strut with its
center at 1518 tangentially intersecting the circular strut with its
center at 1520 to form node 1502d. FIG. 16 illustrates a 3-D
representation of an exemplary embodiment of the porous structure of the
present invention comprising one or more frame configurations in FIGS.
13A-13M, including frames for struts that are straight, curved, or a
combination of both.

[0095] FIG. 17 illustrates a 3-D representation of an exemplary frame for
a generally cubical cell 1700 formed by twelve struts 1702 and sixteen
nodes 1704. Again, for simplification purposes, only some of the struts
and nodes are labeled. By using sixteen nodes 1704 that form connections
between only two struts 1702 as opposed to eight nodes that form
connections between three struts as in a conventional cube design (not
shown), the cell 1700 provides stronger nodes 1704, and stronger
connections between the struts 1702 and nodes 1704. As a result, this
novel configuration of one embodiment of the present invention avoids
variations in cross-sectional diameters between struts 1702 and nodes
1704. As a result, the negative effects of stress risers like those shown
at stress risers 106 and 114 in FIGS. 1A-1B on the strength of the
structure are lessened. FIG. 18 illustrates a porous structure 1800
formed from a plurality of connected cells 1802, which are similar to
those shown in FIG. 17. Similarly, FIGS. 19-20 show another comparison
between the arrangement of cells of the prior art in FIG. 19 and one
embodiment of the arrangement of cells of the present invention in FIG.
20. As previously discussed, by having more than two struts intersect at
a node, the porous structure of the prior art is weak due to the
increased effect of the stress risers. On the other hand, the arrangement
in FIG. 20 of the present invention provides the requisite porosity with
an improved strength because no more than two struts intersect at a node.
In addition, the arrangement of FIG. 20 has the added benefit of having
more trabecular features, resembling the characteristics of cancellous
bone, unlike the regular prior art configuration. Moreover, the advantage
of looking trabecular while being formed in a calculated manner provides
another benefit to the porous structures formed in accordance with the
invention: a decreased need for expansive randomization of the porous
structure. Consequently, the arrangement of FIG. 20 resembles the
characteristics of bones more so than the prior art configuration of FIG.
19. FIG. 21 is a blown up view of the arrangement in FIG. 20 where the
dashed lines 2102 represent the frames of the struts to better show where
the struts meet to form a node.

[0096] Similarly, FIG. 22 illustrates another embodiment of a cell of the
present invention. Cell 2200 is based on a tetrahedron-shaped cell, or a
triangular pyramid, where it is formed using only six struts 2202 and
eight nodes 2204. Each node 2204 connects only two struts 2202 together.
FIG. 23 illustrates a similar cell 2300, which is a square-based pyramid.
Referring to FIG. 23, eight struts 2302 and eleven nodes 2304 are used to
form the cell 2300. Other geometrical shapes for cells, such as
dodecahedrons, icosahedrons, octagonal prisms, pentagonal prisms, cuboids
and various random patterns are discussed below. In addition, FIGS. 17,
18, 22 and 23 illustrate frames of struts that can be built from these
frames where the thickness of each strut can be selected. As such, the
thickness for each strut can be uniform or vary from one strut to another
strut. Further, the struts can incorporate the fluted struts of FIGS.
6-8. In addition, the struts do not have to be cylindrical in shape. As
further discussed below, the cross-section of the struts can be
rectangular or square or any other shape, e.g., geometric shape or
irregular shapes, that would be suitable for the application.

[0097] As discussed above with respect to FIGS. 17, 18, 22, and 23,
various cell designs of various shapes can be created using various
techniques discussed above, e.g., DMF. Generally speaking, almost any
three-dimensional multiple-sided design may be employed. For example,
cells with an overall geometric shape such as Archimedean shapes,
Platonic shapes, strictly convex polyhedrons, prisms, anti-prisms and
various combinations thereof are within the contemplation of the present
invention. In other embodiments, the number of sides of each cell may
range from about 4 to about 24. More preferably, the number of sides of
each cell may range from about 4 to about 16. One geometry that has been
found to be particularly effective is a dodecahedron or 12 sided cell.
However, as explained and illustrated below, the geometries of the
individual cells or the cells of the porous structure may vary widely and
in the geometries may vary randomly from cell to cell of a porous
structure.

[0098] For example, FIGS. 24A and 24B illustrate a conventionally designed
dodecahedral cell 2400 from a prior art porous structure with each node
2404 being a connection between three struts 2402. Again, U.S.
Publication Nos. 2006/0147332 and 2010/0010638 disclose examples of
porous structures formed from these conventional cells. A porous
structure with a given porosity and having a desired volume can be formed
using a plurality of cells 2400 by attaching one cell 2400 to another
cell 2400 until the desired volume is achieved. Further, the structures
using the prior art cell configuration may be disadvantageous because
they do not resemble the randomness of native cancellous structures. That
is, they do not adequately resemble the features of trabecular bone. More
importantly, referring to FIGS. 24A and 24B, higher stresses are placed
at each node 2404 because the struts 2402 intersect one another at
120° angles, thereby increasing stress concentration factors due
to the formation of notches or grooves on the face of the nodes 2404 and
the connection between more than two struts 2402 at each node 2404.

[0099] FIGS. 25A and 25B illustrate one embodiment of the present
invention that provides a solution to these problems of the prior art. As
shown by FIGS. 25A and 25B, cell 2500 eliminated the conventional nodes
2404 in FIGS. 24A and 24B by using curved struts 2502 that form a ring or
hoop, thereby eliminating the stress concentration factors caused by
these nodes. In addition, cells 2500 replace conventional nodes 2404 in
FIGS. 24A and 24B with modified nodes 2504 that can be open or porous to
provide additional porosity, which is an added benefit for many
applications, such as enhancing tissue/bone ingrowth for orthopeadic
implants. Accordingly, cell 2500 provides additional strength with
increased porosity while the conventional cell 2400 is weaker and less
porous.

[0100] FIGS. 26-28 illustrate one embodiment to forming the cell in FIGS.
25A and 25B. FIG. 26 illustrates a dodecahedral frame 2600 for prior art
cells as discussed with respect to FIGS. 24A and 24B. FIG. 27 illustrates
frame 2700 which comprises frame 2800 of FIG. 28 superimposed over the
dodecahedral frame 2600 of FIG. 26. FIG. 29A illustrates a cell similar
to that of FIGS. 25A and 25B formed by selecting a thickness for frame
2800. In FIG. 29A, the cell 2900 is constructed from twelve curved struts
2902 that, in this embodiment, may form a ring, a loop, an annulus, or a
hoop. The curved struts 2902 are joined together at triangular modified
nodes 2904 that are more easily seen in FIG. 29B. Referring to FIG. 29B,
the thicker circles represent four of the curved struts 2902 of the cell
2900 while the thinner circles highlight the modified nodes 2904 formed
by struts 2902. Each modified node 2904 includes three fused connections
or sintering junctions 2906 between two different curved struts 2902.
That is, curved struts 2902 tangentially intersect one another at the
respective junction 2906. Depending on the thickness of each strut 2902,
modified node 2904 may also be porous with openings 2908 disposed between
the three junctions 2906 or occluded with no openings disposed between
the three junctions 2906. Preferably, modified node 2904 has openings
2908 disposed between the three junctions 2906 to provide additional
porosity in conjunction with the porosity provided by the fenestrations
2910 of the curved struts 2902. Referring to FIG. 29B, while the struts
2906 tangentially intersect one another, e.g., their frame tangentially
meet, the struts' thickness may render the individual junctions 2906
relatively long as indicated by the distance 2912. These long, generally
tangential sintering junctions 2906 provide increased mechanical strength
and bonding.

[0101] Referring to FIG. 30, it depicts an unfolded or flattened
two-dimensional representation of FIG. 27, with conventional frame 3008
and the frame 3010 of cell 2900. As shown by FIG. 30, the location and
number of individual junctions 3006, as compared to conventional nodes
3004 of the conventional configuration 3008, is different when using
curved struts 3002 provided by the invention. For example, junctions 3006
are generally located around the center of the body of curved struts
3002, while conventional nodes 3002 is located at the end of the
conventional struts. In addition, in this particular embodiment, the
number of junctions 3006 where the curved struts 3002 meet is three times
the number of conventional nodes 3004 where straight struts meet for
frame 3008. Accordingly, the increased number of junctions provide
increased mechanical strength.

[0102] FIGS. 31-34 illustrate how frames for cells based on a typical
polyhedron can be modified with curved struts to form a cell similar to
cell 2900 of FIG. 29. Specifically, FIG. 31 illustrates a frame 3100 of a
truncated tetrahedral cell unfolded into a 2-D representation. In FIG.
32, frame 3202 represents frame 3100 of FIG. 31 as modified by one
embodiment the present invention to be formed with curved struts 3202.
Similarly, FIG. 33 illustrates the frame 3300 of a truncated octahedral
cell unfolded into a 2-D representation, and frame 3402 of FIG. 34
represents frame 3300 of FIG. 31 as modified by one embodiment the
present invention to be formed with curved struts 3402. As discussed
above, e.g., with respect to FIG. 30, the cells formed with frames 3200
and 3400 have increased mechanical strength and porosity over frames 3100
and 3300, respectively.

[0103] FIGS. 35A-35E illustrate one way of modifying a typical polyhedron
frame with curved struts. According to one embodiment of the invention,
the polyhedron can be modified by inscribing, within the polyhedron, a
circle or other shapes that contain curved features, such as an ellipse
or oblong. Specifically, FIG. 35A is a circle inscribed within a square,
FIG. 35B is a circle inscribed within a hexagon, FIG. 35C is a circle
inscribed within a triangle, FIG. 35D is a circle inscribed within an
octagon, and FIG. 35E is an oval inscribed within a parallelogram. FIGS.
35A-35E are merely demonstrative of the different configurations
available and are not intended to limit the scope of the invention.

[0104] FIG. 36 illustrates another way of modifying a typical polyhedron
frame with curved struts. According to another embodiment of the
invention, the polyhedron can be modified by circumscribing the
polyhedron with a circle or other shapes that contain curved features,
such as an ellipse or oblong. FIG. 36 illustrates a frame 3600 of a
truncated tetrahedral cell with circles 3602 circumscribed around each
face of the cell. Some or all portions of frame 3600 may be removed to
form a new cell frame that can be used to fabricate a porous structure
according to the present invention.

[0105] FIGS. 37-39 illustrate embodiments of the present invention that
incorporate both straight and curved struts. Specifically, FIGS. 37A and
37B illustrate cell 3700 formed from frame 2700 of FIG. 27, which is a
combination of the dodecahedral frame 2600 of FIG. 26 with frame 2800 of
FIG. 28. Cell 3700 has increased strength due to the addition of the
curved struts, which result in a blending of the stress risers. As shown,
cell 3700 has modified node 3704 comprising a conventional node formed
with straight struts 3702b and a node formed by three junctions of the
curved struts 3702a. FIG. 38 illustrates cell 3800 formed by keeping one
or more conventional nodes 3804 formed by straight struts 3802 while
modifying the other struts of the cells with curved struts 3806 to form
junctions 3808 and modified nodes 3810. In FIG. 38 some struts are
selectively thicker than other struts, depending on applications.

[0106] Referring to FIG. 38, the cell 3800 has at least one curved strut
3802, and preferably a plurality of curved struts 3802 that form modified
node 3804a when joined with two other curved struts 3802. In other
embodiments, the modified nodes can be formed by joining together curved
struts, curved strut sections, straight struts, or straight strut
sections, or combinations thereof. An example of a node formed by joining
together straight and curved struts is shown in FIGS. 39A-39C as modified
node 3904b. Modified nodes 3804a are preferably triangular formed by
three junctions 3806. Cell 3800 may contain some convention nodes 3808
that join straight struts 3810 or straight strut sections that may
comprise notches formed by intersecting angles practiced in the prior
art. The modified node 3804a may be porous as discussed previously and
indicated by 3804a or occluded as indicated at 3804b. The occluded
modified nodes 3804b and the porous modified nodes 3804a may be formed by
tangent sintering three or more junctions 3806 between curved or
"ring-like" struts together. Any combination of occluded nodes 3804b,
porous modified nodes 3804a, conventional nodes 3808, straight struts
3810, curved struts 3802, and portions or segments thereof may be used in
different predetermined or random ways in order to create stronger, more
cancellous-appearing cell structure. Referring to FIGS. 39A-39C, cell
3900 is an example of such combination. Cell 3900 has curved struts 3902a
that are "ring-like" and struts 3902b. It also has straight struts 3906
and conventional nodes 3908. The combination of struts forms porous
modified nodes 3904a and occluded modified nodes 3904b.

[0107] Thus, while the cells 3800 within a porous structure may be
homogeneous, they may be arranged in a random and/or predetermined
fashion with respect to each other to more closely resemble the
appearance of cancellous bone. In some instances, it may be desirable to
utilize one or more heterogeneous cell configurations which may be
arranged systematically in predetermined patterns and/or arranged in
random fashion to create a porous structure. Various arrangements can be
designed using computer aided design (CAD) software or other equivalent
software as will be apparent to those skilled in the art.

[0108] FIGS. 40 and 41 show exemplary configurations of how the cells
2400, 2900, and 3700 from FIGS. 24, 29, and 37, respectively, can be
combined, e.g., attached, joined, tiled, stacked, or repeated.
Specifically, FIG. 40 illustrates arrangement 4000 comprising cell 2400
and cell 2900 from FIGS. 24 and 29, respectively. In arrangement 4000, at
the face where cell 2400 attaches to cell 2900, conventional nodes 2404
is placed partially within modified nodes 2904. Accordingly, by using
various combinations of cells 2400 and cells 2900, or other cells formed
according to the present invention, a number of modified nodes 2504 can
be selectively occluded completely or partially by matching conventional
nodes with modified nodes. FIGS. 41A and 41B illustrate arrangement 4100
comprising cells 2400, 2900, and 3700. Again, FIGS. 40 and 41 are
illustrative and do not limit the combination that can be made with these
cells or other cells formed according to the embodiments of the present
invention.

[0109] FIG. 42 illustrates a porous structure 4200 formed by joining a
plurality of cells 4202 together, where the shape of cells 4202 is based
on a truncated tetrahedron. One or more curved struts 4204 which may or
may not form complete rings are inscribed within, or circumscribed
around, each face of the selected polyhedral shape, which is a truncated
tetrahedron in FIG. 42. Alternatively, the truncated tetrahedron shape or
other selected polyhedral shape may be formed using a large number of
short straight struts to closely approximate truly curved ring struts,
such as the ring struts of cell 2900 in FIG. 29.

[0110] FIGS. 43-45 illustrate 3-D representations of exemplary
arrangements cells formed in accordance with the embodiments of the
present invention. Specifically, FIG. 43 illustrates one way cells based
on truncated octahedra can be stacked to form bitruncated cubic honeycomb
structure 4300, which is by space-filling tessellation. The cells of
structure 4300 in both shades of gray are truncated octahedra. For
simplification purposes, each cell is not modified with a curved strut
but rather the dashed circle serves to illustrate that one or more faces
of one or more truncated octahedra can be modified according to the
embodiments of the present invention, e.g., curved struts to form porous
structures with increased strength and porosity. Similarly, FIG. 44
illustrates one way, e.g., space-filling tessellation, cells based on a
combination of cubes (light grey), truncated cuboctahedra (black), and
truncated octahedra (dark grey) can be stacked to form cantitruncated
cubic honeycomb structure 4400. Again, it is understood that the dashed
circles represent how one or more polyhedron of porous structure 4400 can
be modified according to the embodiments of the present invention, e.g.,
curved struts to form porous structures with increased strength and
porosity. Likewise, FIG. 45 illustrates one way, e.g., space-filling
tessellation, cells based on a combination of cuboctahedra (black),
truncated octahedra (dark grey) and truncated tetrahedra (light grey) can
be stacked to form truncated alternated cubic honeycomb structure 4500.
Again, it is understood that the dashed circles represent how one or more
polyhedron of structure 4500 can be modified according to the embodiments
of the present invention, e.g., curved struts to form porous structures
with increased strength and porosity.

[0111] FIG. 46 illustrates a frame view of the bitruncated cubic honeycomb
structure 4300 of FIG. 43. FIG. 47 illustrates a frame view
cantitruncated cubic honeycomb structure 4500 of FIG. 45. As shown by
FIGS. 46 and 47, porous structures formed with polyhedral are not random,
and thus, are not as suitable for implantation purposes, particularly for
bones, because they do not adequately resemble the features of trabecular
bone. On the other hand, as it can be envisioned that modifying certain
or all cells of the frames in FIGS. 46 and 47 would result in porous
structures resembling trabecular bone.

[0112] When curved struts are employed, at least one curved strut portion
may generally form a portion of a ring which at least partially inscribes
or circumscribes a side of a polyhedron. Such a polyhedral shape may be
any one of isogonal or vertex-transitive, isotoxal or edge-transitive,
isohedral or face-transitive, regular, quasi-regular, semi-regular,
uniform, or noble. Disclosed curved strut portions may also be at least
partially inscribed within or circumscribed around one or more sides of
one or more of the following Archimedean shapes: truncated tetrahedrons,
cuboctahedrons, truncated cubes (i.e., truncated hexahedrons), truncated
octahedrons, rhombicuboctahedrons (i.e., small rhombicuboctahedrons),
truncated cuboctahedrons (i.e., great rhombicuboctahedrons), snub cubes
(i.e., snub hexahedrons, snub cuboctahedrons either or both chiral
forms), icosidodecahedrons, truncated dodecahedrons, truncated
icosahedrons (i.e., buckyball or soccer ball-shaped),
rhombicosidodecahedrons (i.e., small rhombicosidodecahedrons), truncated
icosidodecahedrons (i.e., great rhombicosidodecahedrons), snub
dodecahedron or snub icosidodecahedrons (either or both chiral forms).
Since Archimedean shapes are highly symmetric, semi-regular convex
polyhedrons composed of two or more types of regular polygons meeting in
identical vertices, they may generally be categorized as being easily
stackable and arrangeable for use in repeating patterns to fill up a
volumetric space.

[0113] In some embodiments, curved strut portions according to the
invention are provided to form a porous structure, the curved strut
portions generally forming a ring strut portion at least partially
inscribing within or circumscribing around one or more polygonal sides of
one or more Platonic shapes (e.g., tetrahedrons, cubes, octahedrons,
dodecahedrons, and icosahedrons), uniform polyhedrons (e.g., prisms,
prismatoids such as antiprisms, uniform prisms, right prisms,
parallelpipeds, and cuboids), polytopes, polygons, polyhedrons,
polyforms, and/or honeycombs. Examples of antiprisms include, but are not
limited to square antiprisms, octagonal antiprisms, pentagonal
antiprisms, decagonal antiprisms, hexagonal antiprsims, and dodecagonal
antiprisms.

[0115] In some embodiments, the average cross section of the cell
fenestrations of the present invention is in the range of 0.01 to 2000
microns. More preferably, the average cross section of the cell
fenestrations is in the range of 50 to 1000 microns. Most preferably, the
average cross section of the cell fenestrations is in the range of 100 to
500 microns. Cell fenestrations can include, but are not limited to, (1)
any openings created by the struts such as the open modified pores, e.g.,
3804a of FIG. 38 or 1104 of FIGS. 11A-11F, created by the junctions,
e.g., 3806 of FIG. 38 or nodes 1102 of FIGS. 11A-11F, or (2) any openings
inscribed by the struts themselves, e.g., 2910 of FIG. 29B. For example,
in embodiments where the cell fenestrations are generally circular, the
average cross section of a fenestration may be the average diameter of
that particular fenestration, and in embodiments where the cell
fenestrations are generally rectangular or square, the average cross
section of a fenestration may be the average distance going from one side
to the opposite side.

[0116] Applying the above principles to other embodiments, FIGS. 51A and
51B illustrate a cell 5100 formed from an octahedron frame shown in FIG.
48 modified according to one embodiment of the present invention, shown
in FIGS. 49-50. In FIG. 49, frame 4900 is formed by inscribing circles
within the faces of frame 4800 in FIG. 48. In FIG. 50, frame 5000 is
formed by removing frame 4800 from frame 4900 of FIG. 49. As shown in
FIG. 49, the frame 5000 generally fits within the octahedron frame 4800.
FIGS. 51A and 51B illustrate the completed cell 5100, which is formed by
selecting a shape and thickness for frame 5000 in FIG. 50. Referring to
FIGS. 51A and 51B, cell 5100 generally comprises eight curved struts 5102
that may be provided in the form of rings. The eight curved struts 5102
are connected to one another at twelve different junctions 5106. Six
porous modified nodes 5104, each modified node having a generally
rectangular shape are formed by the four different junctions 5106 and the
corresponding struts 5102. As shown by FIGS. 51A and 51B, unlike the
curved struts of cell 2500 of FIGS. 25A and 25B, curved struts 5102 have
a rectangular or square cross-section rather than a circular
cross-section of cells similar to cells 2500 in FIGS. 25A and 25B. Cells
with a rectangular or square cross-section provide the porous structure
with a roughness different than that of the cells with a circular
cross-section. It is envisioned that struts of other embodiments can have
different shapes for a cross-section. Accordingly, the struts of a cell
can have the same cross-section, the shape of the cross-section of the
struts can be randomly chosen, or the cross-section shape can be
selectively picked to achieve the strength, porosity, and/or roughness
desired.

[0117] As another alternative, FIGS. 53A-53D illustrate yet another cell
5300 based on a truncated tetrahedron frame shown in FIG. 52 as modified
by one embodiment of the present invention. Referring to FIGS. 53A-53D,
the cell 5300 is formed in a similar manner to cell 5100 of FIGS. 51A and
51B. That is, frame 5200 is inscribed with circles to form a second frame
comprising circular struts, and frame 5200 is removed leaving behind the
circular frame. Cell 5300 is completed by selecting a thickness and shape
of the cross-sectional area for the frame 5300. As discussed above, the
thickness and shape of the cross-section of the struts can be uniform or
it can vary randomly or in a predetermined manner, including struts with
a uniform cross-section or struts that are fluted. Cell 5300 includes
four larger curved struts 5302a that correspond with the four large
hexagonal sides of the truncated tetrahedral frame 5200 and four smaller
curved struts 5202b that correspond with the four smaller triangular
sides of the truncated tetrahedral frame 5200. Alternative, a cell can be
formed by circumscribing a circle about the large sides 5202 and small
sides 5204 of the truncated tetrahedral frame 5200. A 2-D representation
of this alternative embodiment is shown in FIG. 36. While not expressly
shown in the drawings, it is also contemplated that in some embodiments,
combinations of inscribed and circumscribed curved struts may be
employed. As illustrated in FIGS. 53A-53D, porous triangular modified
nodes 5304 are formed between three junctions 5306 that connect the
struts 5202a and 5202b together, but those skilled in the art will
recognize that occluded modified nodes 3804b as shown in FIG. 38 may also
be employed. Also, as shown in FIGS. 53A-53D, larger curved struts 5302a
have a circular cross-section while smaller curved struts 5302b have a
rectangular cross-section. FIGS. 54A-54E illustrate various angles of a
porous structure formed by stacking cells 5300 of FIG. 53 in one
exemplary manner. It is envisioned that that in some embodiments, cells
5300 of FIG. 53 can be stacked in different manners as known be a person
skilled in the art.

[0118] FIGS. 55A-55E illustrate yet another embodiment where a cell 5500
is based on a hexagonal prism (Prismatic) frame with upper and lower
hexagons and that includes six vertical sides. The six smaller curved
struts 5502a are used for the six sides and larger upper and lower curved
struts 5502b are used for the top and bottom. In the cell 5500
illustrated in FIGS. 55A-55E, the eight curved struts 5302a, 5302b are
connected by occluded modified nodes 5504 but, it will be apparent to
those skilled in the art that porous modified nodes such as those shown
in FIG. 25 may also be employed. In the particular embodiment shown in
FIGS. 55A-55E, the six smaller curved struts 5502a used for the six sides
have a slightly smaller cross-sectional area than the two larger upper
and lower curved struts 5302b. However, it would be apparent to those
skilled in the art that the struts with uniform or substantially uniform
cross-sectional areas can also be employed without departing from the
scope of this disclosure. FIGS. 56A-56B illustrate various angles of a
porous structure formed by stacking cells 5500 of FIGS. 55A-55E in one
exemplary manner. In FIGS. 56A and 56B, cells 5500 are placed adjacent to
one another to form a layer 5602 and the layers are placed on top of one
another either in a predetermined or random manner. FIGS. 57A and 57B
similarly show a greater number of cells 5500 stacked in the same manner
as shown in FIGS. 56A and 56B. As seen, cells 5500 are stacked by layers
5702. It is envisioned that in some embodiments, cells 5500 of FIG. 55
can be stacked in different manners as known to a person skilled in the
art.

[0119] FIGS. 58-61 illustrate dodecahedral frames 5800, 5900, 6000, and
6100 modified according to another embodiment of the invention. Instead
of using curved struts or struts with curved portions to eliminate or
reduce conventional nodes 5802, 5902, 6002, and 6102, the particular
embodiments of FIGS. 58-61 adjust the conventional nodes by ensuring at
least one of the conventional nodes have no more than two nodes
intersecting at a node as shown by at least FIGS. 11A-11F. As shown by
FIGS. 58-61, frames 5800, 5900, 6000, and 6100 have at least one modified
node 5804, 5904, 6004, and 6104.

[0120] In some embodiment, the configurations of the cells, struts, nodes
and/or junctions may vary randomly throughout the porous structure to
more closely simulate natural bone tissue. Particularly, the cells formed
according to the present invention, such as the cells illustrated in
FIGS. 25A-25B, 29A, 37A-37B, 38, 39A-39C, 42, 51A-51B, 53A-53D, or
55A-55B, can be stacked or repeated according to the methods outlined in
U.S. Application No. 61/260,811, the disclosure of which are incorporated
by reference herein in its entirety. In addition, the methods of U.S.
Application No. 61/260,811 can also be employed to modify conventional
nodes such that no more than two struts intersect at a node. In yet
another embodiment, the porous structure formed according to the
invention can be used in medical implants, such as an orthopedic implant,
dental implant or vascular implant.

[0121] As further discussed in the following paragraphs, the present
disclosure also provides for a method to fabricate the porous structures
described above. Preferably, the improved porous structures of the
present invention is formed by using a free-from fabrication method,
including rapid manufacturing techniques (RMT) such as direct metal
fabrication (DMF). Generally, in free-form fabrication techniques, the
desired structures can be formed directly from computer controlled
databases, which greatly reduces the time and expense required to
fabricate various articles and structures. Typically in RMT or free-form
fabrication employs a computer-aided machine or apparatus that has an
energy source such as a laser beam to melt or sinter powder to build the
structure one layer at a time according to the model selected in the
database of the computer component of the machine.

[0122] For example, RMT is an additive fabrication technique for
manufacturing objects by sequential delivering energy and/or material to
specified points in space to produce that part. Particularly, the objects
can be produced in a layer-wise fashion from laser-fusible powders that
are dispensed one layer at a time. The powder is fused, melted, remelted,
or sintered, by application of the laser energy that is directed in
raster-scan fashion to portions of the powder layer corresponding to a
cross section of the object. After fusing the powder on one particular
layer, an additional layer of powder is dispensed, and the process is
repeated until the object is completed.

[0123] Detailed descriptions of selective laser sintering technology may
be found in U.S. Pat. Nos. 4,863,538; 5,017,753; 5,076,869; and
4,944,817, the disclosures of which are incorporated by reference herein
in their entirety. Current practice is to control the manufacturing
process by computer using a mathematical model created with the aid of a
computer. Consequently, RMT such as selective laser re-melting and
sinering technologies have enabled the direct manufacture of solid or 3-D
structures of high resolution and dimensional accuracy from a variety of
materials.

[0124] In one embodiment of the present invention, the porous structure is
formed from powder that is selected from the group consisting of metal,
ceramic, metal-ceramic (cermet), glass, glass-ceramic, polymer, composite
and combinations thereof. In another embodiment, metallic powder is used
and is selected from the group consisting of titanium, titanium alloy,
zirconium, zirconium alloy, niobium, niobium alloy, tantalum, tantalum
alloy, nickel-chromium (e.g., stainless steel), cobalt-chromium alloy and
combinations thereof.

[0125] As known by those skilled in the art, creating models of cells or
structures according to the disclosure of the present invention can be
done with computer aided design (CAD) software or other similar software.
In one embodiment, the model is built by starting with a prior art
configuration and modifying the struts and nodes of the prior art
configuration by either (1) adjusting the number struts that intersect at
a node, such as the configurations in FIGS. 3-8, 11A-11F, 12A-12D, 17-20,
or 22-23, or (2) introduce curved portions to the struts such as the
configurations in FIGS. 13A-13M, 14, 15A-15C, 16, or 58-61. In another
embodiment, curved "ring-like" struts can be added to form cells
illustrated in FIGS. 25A-25B, 29A, 37A-37B, 38, 39A-39C, 42, 51A-51B,
53A-53D, or 55A-55B. Referring to FIG. 26, in one embodiment, these cells
can be formed by starting with a frame 2600 based on a polyhedron, such
as a dodecahedron. Referring to FIG. 27, the next step is to inscribe
circles within each face of the frame 2600 to form frame 2700, which is
frame 2800 superimposed on frame 2600. Subsequently, frame 2600 can be
removed from frame 2700, leaving only frame 2800. The thickness and shape
of the cross-section of frame 2800 can be selected to form a completed
cell, such as cell 2900 in FIG. 29A. As discussed above, a portion of the
faces of frame 2600 can be inscribed with circles and/or a portion of
frame 2600 can be removed to form, or frame 2600 is not removed at all.
The cells formed by such combinations are illustrated in FIGS. 37A-37B,
38, and 39A-39C. As shown by FIGS. 48-53 and 55, the same steps can be
applied to any type of frames based on a polyhedron. Also with the aid of
computer software, stacking, tiling or repeating algorithm can be applied
to create a model of a porous structure with the desired dimensions
formed from unit cells or struts and nodes of the present invention. One
such stacking algorithm is space filling tessellation shown by FIGS.
43-45. As mentioned above, the methods disclosed in U.S. Application No.
61/260,811, which is incorporated by reference herein in its entirety,
can be applied to stack the cells of the present invention or to form the
struts according to the disclosures of the present invention by
controlled randomization.

[0126] Although the present invention and its advantages have been
described in detail, it should be understood that various changes,
substitutions and alterations can be made herein without departing from
the spirit and scope of the invention as defined by the appended claims.
Moreover, the scope of the present application is not intended to be
limited to the particular embodiments of the process, machine,
manufacture, composition of matter, means, methods and steps described in
the specification. As one of ordinary skill in the art will readily
appreciate from the disclosure of the present invention, processes,
machines, manufacture, compositions of matter, means, methods, or steps,
presently existing or later to be developed that perform substantially
the same function or achieve substantially the same result as the
corresponding embodiments described herein may be utilized according to
the present invention. Accordingly, the appended claims are intended to
include within their scope such processes, machines, manufacture,
compositions of matter, means, methods, or steps.